If the seven-digit number $854n526$ is divisible by $11$, what is $n$?
Solution: A number is divisible by $11$ if and only if the sum of the first, third, fifth, etc., digits less the sum of the second, fourth, sixth, etc., digits is itself a multiple of $11$. The former sum is $8+4+5+6=23$. The latter sum if $5+n+2=7+n$. Thus $23-(7+n)=16-n$ must be a multiple of $11$. This is satisfied only by $n=\boxed{5}$.